Answer:
It seems like there might be a typo in your question; I assume you're referring to Chebyshev's Theorem, which is used to make statements about the proportion of data that falls within a certain number of standard deviations from the mean in any data distribution, regardless of its shape.
Chebyshev's Theorem states that for any continuous probability distribution:
1. At least (1 - 1/k^2) of the data falls within k standard deviations of the mean, where k is any positive constant greater than 1.
In your case, you have a mean of 68 points and a standard deviation of 4 points. You want to apply Chebyshev's Theorem with k = 2.
1. k = 2, so k^2 = 4.
2. (1 - 1/k^2) = (1 - 1/4) = 3/4.
So, according to Chebyshev's Theorem with k = 2:
At least 75% (3/4) of the exam scores fall within 2 standard deviations of the mean.
Now, let's calculate the range within which at least 75% of the scores fall:
Lower bound = Mean - (k * Standard Deviation) = 68 - (2 * 4) = 68 - 8 = 60 points
Upper bound = Mean + (k * Standard Deviation) = 68 + (2 * 4) = 68 + 8 = 76 points
Therefore, at least 75% of the exam scores fall between 60 and 76 points.
In summary, using Chebyshev's Theorem with k = 2, you can conclude that at least 75% of the exam scores fall within the range of 60 to 76 points.
Explanation: